Evolutionarily Stable Stackelberg Equilibrium
arXiv:2603.18385
The paper introduces the evolutionarily stable Stackelberg equilibrium (SESS), a solution concept for leader‑follower games where the leader chooses a mixed strategy anticipating that a symmetric population of followers will play an evolutionarily stable strategy, and provides algorithms to compute it.
Abstract
We present a new solution concept called evolutionarily stable Stackelberg equilibrium (SESS). We study the Stackelberg evolutionary game setting in which there is a single leading player and a symmetric population of followers. The leader selects an optimal mixed strategy, anticipating that the follower population plays an evolutionarily stable strategy (ESS) in the induced subgame and may satisfy additional ecological conditions. We consider both leader-optimal and leader-pessimal selection among ESSs, which arise as special cases of our framework. Prior approaches to Stackelberg evolutionary games either define the follower response via evolutionary dynamics or assume rational best-response behavior, without explicitly enforcing stability against invasion by mutations. We present algorithms for computing SESS in discrete and continuous games, and validate the latter empirically. Our model applies naturally to biological settings; for example, in cancer treatment the leader represents the physician and the followers correspond to competing cancer cell phenotypes.